Find the inverse, if it exists, of the given matrix.
-$\mathrm{A}=\left[\begin{array}{ll}4 & 0 \ 2 & 3\end{array}\right]$
A)$\left[\begin{array}{ll}\frac{1}{4} & 0 \ \frac{1}{6} & \frac{1}{3}\end{array}\right]$
B)$$\left[\begin{array}{cc}
\frac{1}{4} & 0 \
-\frac{1}{6} & \frac{1}{3}
\end{array}\right]$$
C) No inverse
D)$$\left[\begin{array}{cc}
\frac{1}{3} & 0 \
-\frac{1}{6} & \frac{1}{4}
\end{array}\right]$$

Question

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$ is $\frac{1}{ad-bc}\begin{bmatrix} d & -b \ -c & a \end{bmatrix}$ if $ad-bc \neq 0$. For matrix A, the determinant is $4*3 - 0*2 = 12$. The inverse is $\frac{1}{12}\begin{bmatrix} 3 & 0 \ -2 & 4 \end{bmatrix} = \begin{bmatrix} \frac{1}{4} & 0 \ -\frac{1}{6} & \frac{1}{3} \end{bmatrix}$.

Find the Inverse, If It Exists, of the Given Matrix A=[4023]\mathrm{A}=\left[\begin{array}{ll}4 & 0 \\ 2 & 3\end{array}\right]A=[42​03​]

Find the Inverse, If It Exists, of the Given Matrix $\mathrm{A}=\left[\begin{array}{ll}4 & 0 \\ 2 & 3\end{array}\right]$